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A300415 Expansion of Product_{k>=2} (1 + x^k)/(1 - x^k).

%I A300415 #21 Jan 25 2021 08:01:22
%S A300415 1,0,2,2,4,6,10,14,22,32,46,66,94,130,182,250,340,462,622,830,1106,
%T A300415 1462,1922,2518,3282,4256,5502,7082,9078,11602,14774,18746,23722,
%U A300415 29922,37630,47202,59044,73662,91682,113830,140994,174262,214906,264462,324802,398110,487018,594694
%N A300415 Expansion of Product_{k>=2} (1 + x^k)/(1 - x^k).
%C A300415 Convolution of the sequences A002865 and A025147.
%C A300415 Also number of overpartitions of n without a 1. - _George Beck_, Jan 25 2021
%H A300415 Seiichi Manyama, <a href="/A300415/b300415.txt">Table of n, a(n) for n = 0..10000</a>
%H A300415 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A300415 G.f.: Product_{k>=2} (1 + x^k)/(1 - x^k).
%F A300415 G.f.: (1 - x)/((1 + x)*theta_4(x)), where theta_4() is the Jacobi theta function.
%F A300415 a(n) ~ Pi * exp(Pi*sqrt(n)) / (32*n^(3/2)). - _Vaclav Kotesovec_, Mar 05 2018
%p A300415 g:= (1-x)/((1+x)*JacobiTheta4(0,x)):
%p A300415 S:=series(g,x,101):
%p A300415 seq(coeff(S,x,j),j=0..100); # _Robert Israel_, Mar 05 2018
%t A300415 nmax = 47; CoefficientList[Series[Product[(1 + x^k)/(1 - x^k), {k, 2, nmax}], {x, 0, nmax}], x]
%t A300415 nmax = 47; CoefficientList[Series[(1 - x)/((1 + x) EllipticTheta[4, 0, x]), {x, 0, nmax}], x]
%Y A300415 Cf. A002865, A015128, A025147, A207641, A211971.
%K A300415 nonn
%O A300415 0,3
%A A300415 _Ilya Gutkovskiy_, Mar 05 2018